The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A294651 Least possible value for the highest denominator in the decomposition of unity as a sum of different unitary fractions the greatest of which is 1/n. 2
1, 6, 15, 20, 24, 28, 33, 40, 48, 52, 65, 65, 75, 76, 85, 88, 91, 100, 105, 115, 115, 119, 132, 140, 144, 145, 155, 161, 162, 171, 217, 174, 182, 190, 195, 196, 296, 200, 207, 220, 246, 224, 301, 231, 238, 253, 329, 275, 280, 287, 288, 296, 371, 300, 304, 305 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The decompositions need not be unique. E.g., for a(7) either 1/12 or 1/20 + 1/30 may be used in the decomposition indifferently.
For prime numbers p and any fixed epsilon < 1, a(p) > epsilon*p*log(p) for all sufficiently large p.
LINKS
Jon E. Schoenfield, All unitary decompositions (listed in lexicographic order) for n = 1..30. (Decompositions up to n = 18 originally found by J. Múgica.)
Javier Múgica, Values of a(n)/n.
EXAMPLE
1 = 1/3 + 1/4 + 1/6 + 1/10 + 1/12 + 1/15, and there is no such decomposition starting at 1/3 and having a greatest denominator smaller than 15, so a(3)=15.
CROSSREFS
Cf. A192881, which looks at decompositions with the least possible number of terms. Those from this sequence achieve those bounds up to a(7), with exception of a(3). However, n=7 is likely the last value of n for which this holds.
Cf. A272083.
Sequence in context: A328226 A045848 A335268 * A368309 A044439 A348866
KEYWORD
nonn,nice
AUTHOR
Javier Múgica, Nov 06 2017
EXTENSIONS
a(18)-a(24) from Jon E. Schoenfield, Dec 22 2019
a(25)-a(56) from Jon E. Schoenfield, Jan 01 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 19:36 EDT 2024. Contains 372666 sequences. (Running on oeis4.)